Achromatic lens system

ABSTRACT

An achromatic lens system which comprises a radial type gradient index lens which has a refractive index varying in a direction perpendicular to an optical axis and a diffraction type lens, and sufficiently corrects the secondary spectrum with a small number of optical elements.

BACKGROUND OF THE INVENTION

A) Field of the Invention:

The present invention relates to an achromatic lens system which is tobe used in optical systems for telescopes, microscopes, cameras, videocameras, etc., and an image pickup lens system which comprises anachromatic lens system.

B) Description of the Prior Art

An optical system which is to be used in telescopes, microscopes,cameras, video cameras, etc. generally has a composition in which alarge numbers of lenses are combined for enhancing optical performanceof the optical system. A cemented achromatic lens which is referred toas an achromat is frequently used in optical system for correctingchromatic aberration in particular. This achromat corrects chromaticaberration ordinarily for rays having two wavelengths such as the C-lineand the F-line, but does not strictly correct chromatic aberration forrays having different wavelengths such as the g-line, thereby allowingchromatic aberration which is referred to as the so-called secondaryspectrum to remain. This residual chromatic aberration often posesproblems in objective lens systems for telescopes and microscopes aswell as telephoto lens systems for cameras and so on in particular, anda lens system which is made achromatic for three wavelengths and isreferred to as an apochromat is used for correcting the residualchromatic aberration.

However, it is necessary for manufacturing apochromats to use fluoriteor low dispersion glass materials which have extraordinary dispersioncharacteristics, and are expensive and hard to work, thereby enhancingmanufacturing costs of optical systems.

In addition to ordinary lenses which utilize the refraction phenomenon,there are available lenses which utilize the diffraction phenomenon andare referred to as diffraction type lenses. The diffraction type lenshas a dispersion characteristic which is different from that of theordinary lens. As an example wherein a diffraction type lens is used forcorrecting the secondary spectrum of chromatic aberration, there is anoptical system which consists of a combination of a cemented lens and adiffraction type lens as described in Applied Optics, Vol. 27, pp 2960through 2971.

Furthermore, as another example of lens system wherein chromaticaberration is corrected using a diffraction type lens, there is known alens system such as that disclosed by Japanese Patent Kokai PublicationNo. Hei 4-181908 which uses a combination of a diffraction type lens anda radial type GRIN lens.

An optical system such as that described in the literature mentionedabove (Applied Optics) which consists of a combination of a cementedlens and a diffraction type lens uses three optical elements in total ora large number of optical elements, thereby requiring a highmanufacturing cost. Moreover, the lens system disclosed by the publishedbulletin mentioned above which consists of the radial type GRIN lens andthe diffraction type lens is designed while paying attention only tochromatic aberration of the first order and no description is made ofthe secondary spectrum in the bulletin.

SUMMARY OF THE INVENTION

A primary object of the present invention is to provide an achromaticlens system which elaborately corrects the secondary spectrum ofchromatic aberration with a small number of optical elements.

The achromatic lens system according to the present invention comprisesa radial type gradient index lens (radial type GRIN lens) whoserefractive index varies in a direction perpendicular to an optical axisand a diffraction type optical element (diffraction type lens), and ischaracterized in that it satisfies the following condition (1):

    0.1<θ.sub.e1gF <0.5                                  (1)

The achromatic lens system according to the present invention ischaracterized in that it satisfies the following condition (2):

    67<V.sub.e1 <370                                           (2)

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a sectional view illustrating a fundamental composition ofthe achromatic lens system according to the present invention;

FIG. 2 shows a sectional view illustrating another fundamentalcomposition of the achromatic lens system according to the presentinvention;

FIGS. 3 through 5 show sectional views illustrating compositions offirst through third embodiments of the achromatic lens system accordingto the present invention; and

FIG. 6 shows a sectional view illustrating a composition of aconventional achromatic lens system.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The achromatic lens system according to the present invention comprises,as shown in FIG. 1, a radial type gradient index lens (radial type GRINlens) G whose refractive index varies in a direction perpendicular to anoptical axis and a diffraction type optical element (diffraction typelens) D, and satisfies the following condition (1):

    0.1<θ.sub.e1gF <0.5                                  (1)

wherein the reference symbol θ_(e1gF) represents an equivalent partialdispersion ratio of the radial type GRIN lens.

The radial type GRIN lens is made of a medium which has a refractiveindex distribution in the direction perpendicular to the optical axisand a refractive index distribution N(r) is expressed by the followingformula (a):

    N(r)=N.sub.0 +N.sub.1 r.sup.2 +N.sub.2 r+N.sub.3 r.sup.6 +. . . (a)

Wherein the reference symbol N₀ represents a refractive index on theoptical axis, the reference symbol N_(i) (i=1, 2, 3, . . . ) designatesa coefficient expressing a refractive index distribution and thereference symbol r denotes a distance as measured from the optical axisin the direction perpendicular to the optical axis.

Further, an Abbe's number of a radial type GRIN lens is given by theformulae (b) and (c) which are shown below:

    V.sub.0 =(N.sub.0d -1)/(N.sub.0F -N.sub.0C)                (b)

    V.sub.1 =N.sub.id /(N.sub.iF -N.sub.ic) (i=1, 2, 3, . . . )(c)

Wherein N_(i)λ (i=1, 2, 3, . . . ) represents a coefficient expressing arefractive index distribution at a wavelength λ, and the referencesymbols N_(id), N_(iF) and N_(iC) designate refractive indexdistributions at the wavelengths of the d-line, F-line and C-linerespectively.

Further, partial dispersion ratios θ_(1dC) and θ_(1gF) of a medium of aradial type GRIN lens are given by the following formulae (d) and (e):

    θ.sub.1dC =(N.sub.1d -N.sub.1C)/(N.sub.1F -N.sub.1C) (d)

    θ.sub.1gF =(N.sub.1g -N.sub.1F)/(N.sub.1F -N.sub.1c) (e)

wherein the reference symbol N_(1g) represents a coefficient N₁ whichexpresses a refractive index distribution at the wavelength of theg-line.

Furthermore, a diffraction type lens which has a concentric pattern andexhibits a function of a lens owing to the diffraction phenomenon oflight has a color dispersion characteristic such as an Abbe's number of-3.45 which is extraordinary as compared with that of glass.

The achromatic lens system according to the present invention isconfigured to elaborately correct the residual secondary spectrum ofchromatic aberration by combining the radial type GRIN lens and thediffraction type lens as described above.

FIG. 1 shows a fundamental composition of the achromatic lens systemaccording to the present invention, wherein the lens system is composedby combining a radial type GRIN lens G having two planar surfaces with adiffraction type lens D. Let us represent a power of a medium of theradial type GRIN lens by φ_(m) and designate a power of the diffractiontype lens by φ_(D), and assume that the two lenses are disposed close toeach other as shown in the drawing. Then, chromatic aberration PAC ofthe C-line and F-line produced by this lens system is approximatelygiven by the following formula (f):

    PAC=K{(φ.sub.m /V.sub.1)+(φ.sub.D /V.sub.D)}       (f)

wherein the reference symbol V₁ represents an Abbe's number of medium ofthe radial type GRIN lens, the reference symbol V_(D) designates anAbbe's number of the diffraction type lens and the reference symbol Kdenotes a constant.

Further, chromatic aberration of the g-line for the F-line is given bythe following formula (g):

    PAC(g)=K{(φ.sub.m /V.sub.1)·θ.sub.1gF +(φ.sub.D /V.sub.D)·θ.sub.D }                        (g)

Wherein the reference symbol θ_(1gF) represents a partial dispersionratio of the medium of the radial type GRIN lens and the referencesymbol θ_(D) designates a partial dispersion ratio of the diffractiontype lens for the g-line and the F-line.

Let us consider to make the lens system achromatic for three colors ofthe C-line, F-line and g-line. Since it is necessary for this purpose tozero both the formulae (f) and (g) at same time, θ_(1gF) and θ_(D) musthave the same value.

Since θ_(D) is 0.2956 as described in the literature mentioned above,θ_(1gF) must have the value specified below as a condition required formaking the lens system achromatic for the three colors.

    θ.sub.1gF =0.2956                                    (h)

On the basis of the condition derived here, and in view of facts thatthe lens system is actually thick and that different wavelengths must bebalanced within the visible region other than the three colors, theachromatic lens system according to the present invention is configuredso as to satisfy the condition (3) show below for favorably correctingthe secondary spectrum:

    0.1<θ.sub.1gF <0.5                                   (3)

If the upper limit or the lower limit of the condition (3) is exceeded,it will be impossible to favorably correct the secondary spectrum.

For reducing chromatic aberration strictly at the three wavelengths inthe achromatic lens system according to the present invention, it isdesirable to satisfy, in place of the condition (3), the followingcondition (3-1):

    0.2<θ.sub.1gF <0.4                                   (3-1)

Now, let us consider a partial dispersion ratio θ_(1gF) of the radialtype GRIN lens. According to Herzberger's dispersion formula (see"Optics for Optical Appliances 1-Basis and Design of Optical systems-"pp on and after 395 published by a foundational juridical person JapanOptoelectro Mechanics Association) a refractive index of an opticalglass material is expressed by the following formula (i):

    N(λ)=1+(n.sub.d -1) {1+B(λ)+A(λ)τ.sub.d }(i)

wherein the reference symbols A(λ) and B(λ) represent coefficients whichare dependent only on a wavelength λ, and the reference symbol τ_(d)designates a dispersion ratio which is a reverse number of an Abbe'snumber.

From the formula (i) mentioned above, we can derive the followingformula (j):

    δn(λ)={1+B(λ)+A(λ)τ.sub.d }δn.sub.d +A(λ) (n.sub.d -1)δτ.sub.d               (j)

Assuming that a characteristic of the glass material satisfiesHerzberger's formula within each minute region of a radial type GRINlens and, that coefficients of N₂ and higher orders out of thecoefficients representing a refractive index distribution are small, arefractive index distribution coefficient in the vicinity of an opticalaxis is:

    N.sub.1λ =δn.sub.80 /δr.sup.2

Hence, an Abbe's number of the medium is given by the following formula(l):

    V.sub.1 =N.sub.1d /(n.sub.1F -N.sub.1C)=δn.sub.d /(δn.sub.F -δn.sub.c)

    =δn.sub.d / τ.sub.d δn.sub.d +(n.sub.d -1)δτ.sub.d !                                   (l)

From these formulae (e) and (i), θ_(1gF) is calculated as follows:##EQU1##

It will be understood from this formula that the partial dispersionratio of the medium of the radial type GRIN lens is similar, within theassumed angle, to that of the ordinary glass material which has noextraordinary dispersion characteristic.

On the basis of the foregoing description and the condition (3), it isdesirable that a medium of a radial type GRIN lens which has a lowextraordinary dispersion characteristic satisfies the followingcondition (4):

    67<V.sub.1 <370                                            (4)

If the upper limit or the lower limit of the condition (4) is exceeded,chromatic aberration will be aggravated at the selected threewavelengths, thereby making it difficult to correct the residualsecondary spectrum favorably over the entire visible region or it isnecessary to use a material having an extraordinary dispersioncharacteristic which is largely different from that of the ordinarymaterial for the radial type GRIN lens, thereby making it difficult tomanufacture a material for the radial type GRIN lens.

When a radial type GRIN lens which has an extremely low extraordinarydispersion characteristic is to be used in the achromatic lens systemaccording to the present invention or when the achromatic lens system isto be configured so as to strictly correct the secondary spectrum, it isdesirable to satisfy, in place of the condition (4), the followingcondition (4-1):

    84<V.sub.1 <310                                            (4-1)

If the upper limit or the lower limit of the condition (4-1) isexceeded, the secondary spectrum will remain in a large amount or itwill be obliged to use a material having an extraordinary dispersioncharacteristic which is different from that of the ordinary material forthe GRIN lens, thereby bringing about an undesirable result from aviewpoint of manufacturing of a material.

When chromatic aberration is corrected by satisfying the conditions (3),(3-1), (4) and (4-1), φ_(m) and φ_(D) have the same sign.

FIG. 2 shows a sectional view illustrating another composition of theachromatic lens system according to the present invention, wherein theachromatic lens system consists of a combination of a radial type GRINlens which have curvature on the surfaces thereof and a diffraction typelens. In case of this achromatic lens system, it is necessary to takeinto consideration a refractive power φ_(s) which is produced by thesurfaces of the radial type GRIN lens.

When the radial type GRIN lens has curvature on the surfaces thereof,formulae (m) and (n) which are mentioned below are used in place of theformulae (f) and (g):

    PAC(s)=K (φ.sub.s /V.sub.0)+(φ.sub.m /V.sub.1)+(φ.sub.D /V.sub.D)!                                                (m)

    PAC(sg)=K (φ.sub.s /V.sub.0)θ.sub.0gF +(φ.sub.m /V.sub.1)θ.sub.1gF +(φ.sub.D /V.sub.D)θ.sub.D !(n)

wherein the reference symbols V₀ and θ_(0gF) represent an Abbe's numberand a partial dispersion ratio respectively on the optical axis of theradial type GRIN lens. In addition, θ_(0gF) is expressed by thefollowing formula:

    θ.sub.0gF =(N.sub.0g -N.sub.0F)/(N.sub.0F -N.sub.0C)

wherein the reference symbol N_(0g) represents a coefficient N₀ whichexpresses a refractive index distribution at the wavelength of theg-line.

The conditions (3), (3-1), (4) and (4-1) can be extended to manage thecase where the radial type GRIN lens has the curvature, though themanagement is rather complicated, by using an equivalent partialdispersion ratio θ_(e1gF) which is determined by the formulae (o), (p)and (q) shown below, and an equivalent Abbe's number V_(e1) in place ofθ_(1gF) and V₁ respectively:

    φ=φ.sub.s +φ.sub.m                             (o)

    φ/V.sub.e1 =(φ.sub.s /V.sub.0)+(φ.sub.m /V.sub.1) (p)

    (φ/V.sub.1)θ.sub.e1gF =(φ.sub.s /V.sub.0)θ.sub.0gF +(φ.sub.m /V.sub.1)θ.sub.1gF                    (q)

wherein the reference symbol φ represents a refractive power of theradial type GRIN lens as a whole.

Accordingly, it is desirable that the achromatic lens system accordingto the present invention which is composed of the combination of theradial type GRIN lens having the curvature on the surfaces thereof andthe diffraction type lens satisfies the following conditions (1) and(2):

    0.1<θ.sub.e1gF <0.5                                  (1)

    67<V.sub.e1 <370                                           (2)

Further, it is more preferable to satisfy, in place of the conditions(1) and (2), the conditions (1-1) and (2-1) shown below, thereby makingit possible to obtain an achromatic lens system in which the secondaryspectrum, for example, is corrected strictly:

    0.2<θ.sub.e1gF <0.4                                  (1-1)

    84<V.sub.e1 <310                                           (2-1)

A radial type GRIN lens which has the two planar surfaces has a power ofsurface φ_(s) of 0. In case of φ_(s) =0, these formulae are transformedas follows:

    θ.sub.e1gF =θ.sub.1gF

    V.sub.e1 =V.sub.1

That is to say, the conditions (3) and (4) mentioned above can beobtained by using V₁ and θ_(1gF) in place of V_(e1) and θ_(e1gF)respectively in the conditions (1) and (2). Accordingly, it is desirableto satisfy the conditions (1) and (2) whether a GRIN lens has curvedsurfaces or planar surfaces.

The achromatic lens system according to the present invention which hasbeen described above is usable for composing optical systems not onlyfor telescopes and microscopes but also image pickup system composed bycombining the achromatic lens system with image pickup devices.

Now, description will be made of embodiments of the achromatic lenssystem according to the present invention.

A first embodiment has a composition illustrated in FIG. 3, wherein adiffraction lens is formed on an image side surface of a radial typeGRIN lens which has two planar surfaces. The first embodiment hasspecifications and numerical data which are listed below:

    ______________________________________    f = 10, F/4.0, maximum image height 1.85    ______________________________________    r.sub.1 = ∞ (stop)    d.sub.1 = 6.9489               n.sub.1 (gradient index lens)    r.sub.2 = ∞    d.sub.2 = 0               n.sub.2 = 1001                         ν.sub.2 = -3.45 (diffraction type lens)    r.sub.3 = -2.496 × 10.sup.5    Gradient index lens    N.sub.0 = 1.6640,             N.sub.1 = 7.5000 × 10.sup.-3,                            V.sub.0 = 38.2,                                      V.sub.1 = 104    θ.sub.1dC = 0.30    θ.sub.1gF = 0.34,             θ.sub.e1gF = 0.34,                            V.sub.el = 104    ______________________________________

A second embodiment is composed, in order from the object side as shownin FIG. 4, of a radial type GRIN lens which has two planar surfaces anda diffraction type lens which is formed on a planar glass plate. Thesecond embodiment has specifications and numeral data which are shownbelow:

    ______________________________________    f = 10, F/4.0, maximum image height 1.85    ______________________________________    r.sub.1 = ∞ (stop)    d.sub.1 = 6.7176               n.sub.1 (gradient index lens)    r.sub.2 = ∞    d.sub.2 = 3.0000    r.sub.3 = ∞    d.sub.3 = 2.0000               n.sub.2 = 1.51633                         ν.sub.2 = 64.15    r.sub.4 = ∞    d.sub.4 = 0.0000               n.sub.3 = 1001                         ν.sub.2 = -3.45 (diffraction type lens)    r.sub.5 = -6.696 × 10.sup.4    gradient index lens    N.sub.0 = 1.6640,             N.sub.1 = -7.5000 × 10.sup.-3,                            V.sub.0 = 38.2,                                      V.sub.1 = 101    θ.sub.1dC = 0.30    θ.sub.1gF = 0.35,             θ.sub.e1gF = 0.35,                            V.sub.e1 = 101    ______________________________________

A third embodiment has a composition illustrated in FIG. 5, wherein anachromatic lens system is composed of a radial type GRIN lens which hasa concave object side surface and a planar image side surface, and adiffraction type lens which is formed on an image side surface of theradial type GRIN lens. This achromatic lens system has specificationsand numerical data which are listed below:

    ______________________________________    f = 10, F/4.0, maximum image height 1.85    ______________________________________    r.sub.1 = -10.000  (stop)    d.sub.1 = 7.7588               n.sub.1 (gradient index lens)    r.sub.2 = ∞    d.sub.2 = 0               n.sub.2 = 1001                         ν.sub.2 = -3.45 (diffraction type lens)    r.sub.3 = -3.804 × 10.sup.5    gradient index lens    N.sub.0 = 1.60000,             N.sub.1 = -1.0000 × 10.sup.-2,                            V.sub.0 = 45.00,                                      V.sub.1 = 78    θ.sub.1dC = 0.30    θ.sub.1gF = 0.34,             θ.sub.e1gF = 0.21,                            V.sub.el = 184    ______________________________________

In the numerical data of the three embodiments, that of the diffractiontype lens is specified in a form wherein a refractive index at astandard wavelength of the d-line is taken as 1001 using the so calledultra high refractive index approximation.

FIG. 6 shows an achromatic lens system which has the same specificationsas those for the achromatic lens system according to the presentinvention, but is composed of the ordinary cemented lens and has thefollowing numerical data:

    ______________________________________    f = 10, F/4.0, maximum image height 1.85    ______________________________________    r.sub.1 = 4.0230 (stop)    d.sub.1 = 3.0000                   n.sub.1 = 1.51633                                ν.sub.1 = 64.14    r.sub.2 = -2.9157    d.sub.2 = 1.0000                   n.sub.2 = 1.62004                                ν.sub.2 = 36.26    r.sub.3 = 234.6664    ______________________________________

The first, second and third embodiments of the present invention, andthe achromatic lens system shown in FIG. 6 have longitudinal chromaticaberration listed below:

    ______________________________________           Wavelength           365.01                 435.83  486.13  546.07                                       587.56                                             656.27           nm    nm      nm      nm    nm    nm           i-line                 g-line  F-line  e-line                                       d-line                                             C-line    ______________________________________    Embodiment 1             -0.0142 -0.0075 -0.0075                                   -0.0002                                         0     -0.0075    Embodiment 2             -0.0124 -0.0072 -0.0072                                   -0.0002                                         0     -0.0072    Embodiment 3             -0.0175 -0.0065 -0.0065                                   -0.0001                                         0     -0.0065    Lens system             0.0977  0.0203  0.0046                                   -0.0005                                         0     0.0046    Shown in    FIG. 6    ______________________________________

I claim:
 1. An achromatic lens system comprising: a radial type gradientindex lens which has a refractive index varying in a directionperpendicular to an optical axis; and a diffraction type lens, whereinsaid achromatic lens system satisfies the following condition (1):

    0.1<θ.sub.e1gF <0.5                                  (1)

wherein the reference symbol θ_(e1gF) represents an equivalent partialdispersion ratio of said radial type gradient index lens.
 2. Anachromatic lens system according to claim 1 satisfying the followingcondition (2):

    67<V.sub.e1 <370                                           (2)

wherein the reference symbol V_(e1) represents an equivalent Abbe'snumber of said radial type gradient index lens.
 3. An achromatic lenssystem according to claim 1 satisfying, in place of the condition (1),the following condition (1-1)

    0.2<θ.sub.e1gF <0.4                                  (1-1).


4. An achromatic lens system according to claim 2 satisfying, in placeof the condition (2), the following condition (2-1)

    84<V.sub.e1 <310                                           (2-1).


5. An achromatic lens system according to claim 1, 2, 3 or 4 whereinsaid radial type gradient index lens has two planar surfaces.
 6. Anachromatic lens system according to claim 1, 2, 3 or 4 wherein saidradial type gradient index lens has at least one curved surface.
 7. Anachromatic lens system according to claim 1, 2, 3 or 4 wherein saidradial type gradient index lens has a concave surface on the objectside.
 8. An achromatic lens system according to claim 1, 2, 3 or 4wherein said diffraction type lens is formed on a surface of said radialtype gradient index lens.